Nonlinear relationships
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Nonlinear Relationships. Chapter 7. Prepared by Vera Tabakova, East Carolina University. Chapter 7: Nonlinear Relationships. 7.1 Polynomials 7.2 Dummy Variables 7.3 Applying Dummy Variables 7.4 Interactions Between Continuous Variables 7.5 Log-Linear Models. 7.1 Polynomials.

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Chapter 7

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Nonlinear Relationships

Chapter 7

Prepared by Vera Tabakova, East Carolina University


Chapter 7: Nonlinear Relationships

  • 7.1 Polynomials

  • 7.2 Dummy Variables

  • 7.3 Applying Dummy Variables

  • 7.4 Interactions Between Continuous Variables

  • 7.5 Log-Linear Models

  • Principles of Econometrics, 3rd Edition


    7.1 Polynomials

    7.1.1 Cost and Product Curves

    Figure 7.1 (a) Total cost curve and (b) total product curve

    Principles of Econometrics, 3rd Edition


    7.1 Polynomials

    Figure 7.2 Average and marginal (a) cost curves and (b) product curves

    Principles of Econometrics, 3rd Edition


    7.1 Polynomials

    Principles of Econometrics, 3rd Edition


    7.1.2 A Wage Equation

    If Deriv < 0 => Exper < -β3/2β4 ,

    or Exper> β3/2β4 .

    Principles of Econometrics, 3rd Edition


    7.1.2 A Wage Equation

    Principles of Econometrics, 3rd Edition


    7.1.2 A Wage Equation

    Where 33.47 is the ‘turning point’

    Principles of Econometrics, 3rd Edition


    7.2 Dummy Variables

    Principles of Econometrics, 3rd Edition


    7.2.1 Intercept Dummy Variables

    Principles of Econometrics, 3rd Edition


    7.2.1 Intercept Dummy Variables

    Figure 7.3 An intercept dummy variable

    Principles of Econometrics, 3rd Edition


    7.2.1a Choosing The Reference Group

    Principles of Econometrics, 3rd Edition


    7.2.2 Slope Dummy Variables

    Principles of Econometrics, 3rd Edition


    7.2.2 Slope Dummy Variables

    Figure 7.4 (a) A slope dummy variable. (b) A slope and intercept dummy variable

    Principles of Econometrics, 3rd Edition


    7.2.2 Slope Dummy Variables

    Principles of Econometrics, 3rd Edition


    7.2.3 An Example: The University Effect on House Prices

    Principles of Econometrics, 3rd Edition


    7.2.3 An Example: The University Effect on House Prices

    Principles of Econometrics, 3rd Edition


    7.2.3 An Example: The University Effect on House Prices

    Principles of Econometrics, 3rd Edition


    7.2.3 An Example: The University Effect on House Prices

    Principles of Econometrics, 3rd Edition


    7.2.3 An Example: The University Effect on House Prices

    Based on these regression results, we estimate

    • the location premium, for lots near the university, to be $27,453

    • the price per square foot to be $89.12 for houses near the university, and $76.12 for houses in other areas.

    • that houses depreciate $190.10 per year

    • that a pool increases the value of a home by $4377.20

    • that a fireplace increases the value of a home by $1649.20

    Principles of Econometrics, 3rd Edition


    7.3 Applying dummy variables

    • 7.3.1 Interactions Between Qualitative Factors

    Principles of Econometrics, 3rd Edition


    7.3.1 Interactions Between Qualitative Factors

    Principles of Econometrics, 3rd Edition


    7.3.1 Interactions Between Qualitative Factors

    Principles of Econometrics, 3rd Edition


    7.3.2 Qualitative Factors with Several Categories

    Principles of Econometrics, 3rd Edition


    7.3.2 Qualitative Factors with Several Categories

    Principles of Econometrics, 3rd Edition


    7.3.3 Testing the Equivalence of Two Regressions

    Principles of Econometrics, 3rd Edition


    7.3.3 Testing the Equivalence of Two Regressions

    Principles of Econometrics, 3rd Edition


    7.3.3 Testing the Equivalence of Two Regressions

    Principles of Econometrics, 3rd Edition


    7.3.3 Testing the Equivalence of Two Regressions

    Principles of Econometrics, 3rd Edition


    7.3.4 Controlling for Time

    7.3.4a Seasonal Dummies

    7.3.4b Annual Dummies

    7.3.4c Regime Effects

    Principles of Econometrics, 3rd Edition


    7.4 Interactions Between Continuous Variables

    Principles of Econometrics, 3rd Edition


    7.4 Interactions Between Continuous Variables

    Principles of Econometrics, 3rd Edition


    7.4 Interactions Between Continuous Variables

    Principles of Econometrics, 3rd Edition


    7.4 Interactions Between Continuous Variables

    Principles of Econometrics, 3rd Edition


    7.5 Log-Linear models

    7.5.1 Dummy Variables

    Principles of Econometrics, 3rd Edition


    7.5.1a A Rough Calculation

    Principles of Econometrics, 3rd Edition


    7.5.1b An Exact Calculation

    Principles of Econometrics, 3rd Edition


    7.5.2 Interaction and Quadratic Terms

    Principles of Econometrics, 3rd Edition


    7.5.2 Interaction and Quadratic Terms

    Principles of Econometrics, 3rd Edition


    Keywords

    • annual dummy variables

    • binary variable

    • Chow test

    • collinearity

    • dichotomous variable

    • dummy variable

    • dummy variable trap

    • exact collinearity

    • hedonic model

    • interaction variable

    • intercept dummy variable

    • log-linear models

    • nonlinear relationship

    • polynomial

    • reference group

    • regional dummy variable

    • seasonal dummy variables

    • slope dummy variable

    Principles of Econometrics, 3rd Edition


    Chapter 7 Appendix

    • Appendix 7 Details of log-linear model interpretation

    Principles of Econometrics, 3rd Edition


    Appendix 7 Details of log-linear model interpretation

    Principles of Econometrics, 3rd Edition


    Appendix 7 Details of log-linear model interpretation

    Principles of Econometrics, 3rd Edition


    Appendix 7 Details of log-linear model interpretation

    Principles of Econometrics, 3rd Edition


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